1. Field of the Invention
The present invention generally relates to a gear device and a method of producing such a gear device. More particularly, the invention relates to a gear device which rotates while transferring power from a first gear to a second gear and which has a tooth profile improved in reducing the local frictional heat value. The invention also relates to a method of producing such a gear device.
2. Description of the Related Art
FIGS. 19 and 20 illustrate the configuration obtained by performing two types of the tooth-profile correction on a conventional gear. Portion a indicates a rack-like shape obtained by developing an involute curve for forming the tooth profile of the gear into a straight line. Portion b indicates the configuration obtained by performing the tooth-profile correction over a range of portions g and h. The values g and h are described in general literature of this technical field (which literature is exemplified in the portion marked with "*"; hereinafter). The portions filled in with black indicate those which have been shaved (hereinafter, such portions mean the same). In other words, the outer line including such portions indicates the rack-like shape obtained by developing the involute curve into a straight line, while the inner line excluding such portions indicates the configuration of the tooth profile which has been corrected. The inner line of portion b in FIG. 19 is indicated by a straight line, while that in FIG. 20 is indicated by a circular arc having radius r. FNT *: (1) ISO/TC 60/SC 3/WG 12 Doc N 6
A pair of gears formed in the shape as described above are intermeshed with each other as illustrated in FIG. 21. For transmitting a torque of a gear 1 to a gear 2, the tooth intermeshing starts at point P on the line of action C (length of intermeshing) and ends at point R via points O and Q. FIG. 21 shows a pitch circle d.sub.1 of the gear 1, a pitch circle d.sub.2 of the gear 2, a base circle e.sub.1 of the gear 1, a base circle e.sub.2 of the gear 2, an addendum circle f.sub.1 of the gear 1, an addendum circle f.sub.2 of the gear 2, and pitch point O at which the relative sliding velocity at the tooth surface becomes zero.
The states of intermeshing the gears 1 and 2 from starting point P to end point R will now be explained with reference to FIGS. 22A-22E.
FIG. 22A shows the state in which the gears 1 and 2 are intermeshed at point Q.sub.11 on the line of action C and at which the intermeshing point Q.sub.11 moves to the right-hand of FIG. 22A as indicated by the arrow 3.
FIG. 22B shows the state in which the intermeshing point moves from point Q.sub.11 to point Q.sub.12, and simultaneously, the teeth adjacent to the line of approach start to intermesh with each other at point Q.sub.22.
FIG. 22C shows the state in which the intermeshing point adjacent to the line of recess moves from point Q.sub.12 to point Q.sub.13 and the intermeshing point adjacent to the line of approach moves from point Q.sub.22 to point Q.sub.23, and which the teeth are thus intermeshing with each other at the two points Q.sub.13 and Q.sub.23 at the same time.
FIG. 22D shows the state in which the intermeshing point adjacent to the line of approach moves from point Q.sub.23 to point Q.sub.24, and simultaneously, the teeth adjacent to the line of recess finish intermeshing at point Q.sub.14.
FIG. 22E shows the state in which the intermeshing point adjacent to the line of approach moves from point Q.sub.24 to point Q.sub.25, that is, the gears are intermeshed only at point Q.sub.25.
FIG. 21 shows the intermeshing state of the gears 1 and 2 in which the intermeshing point Q moves on the line of action C in the direction indicated by the arrow 3, and then, the gears 1 and 2 start to be intermeshed at point P.
In such a state, the tooth of the gear 1 intermeshed at point Q is bent and deflected on the line of action C in the direction reverse to that indicated by the arrow 3. At the same time, the gear 2 is bent and deflected on the line of action C in the direction indicated by the arrow 3.
In consequence, the distance between points P and Q of the gear 1 is contracted, while that of the gear 2 is stretched, thus causing an abrupt collision between the teeth of the gears 1 and 2 at point P.
In order to alleviate such a collision, the configuration of the addendum portions is corrected, as shown in FIG. 19 or FIG. 20. This correction is designed in order to avoid an abrupt collision at the initial point P of the gear intermeshing so that a load varies smoothly and in order to minimize a change in the rotation angle to be transmitted.
FIG. 23 shows the state of the intermeshing of the conventional gear illustrated in FIG. 21 and indicates the load F acting on teeth starting from starting point P of the gear intermeshing to end point R via point Q on the line of action C, the relative sliding velocity v at the intermeshing surface of contact, and the product F.multidot.v of the load F and the sliding velocity v. The load F and the sliding velocity v can be calculated based on the general literature (indicated by "*") of this technical field. FNT *: (1) ISO/TC 60/SC 3/WG 12 Doc N 6
In FIG. 23, a curve 4 indicative of the load F acting on the teeth (representing the weight kg by the unit of kgf) and consists of an increasing curve 4a, a straight line 4b indicative of the maximum load, and a decreasing curve 4c. A curve 5 indicates the relative sliding velocity v (by the unit of m/s) at the intermeshing surface of contact and consists of a decreasing curve 5a and an increasing curve 5b which are bordered by pitch point O. A curve 6 indicates the product F.multidot.v of the load F and the relative sliding velocity v and consists of a first curve 6a and a second curve 6b which are bordered by pitch point O, the curves being formed in a projection-like shape.
As is indicated by the increasing curve 4a, a sharp increase in the load F acting on the teeth is alleviated by the tooth-profile correction shown in FIG. 19 or FIG. 20. However, as indicated by the straight line 4b of FIG. 23, when the maximum load is imposed on the teeth, the product F.multidot.v of the load F and the relative sliding velocity v increases as the relative sliding velocity v gradually increases from pitch point O. Even when the intermeshing nearly comes to an end, the decreasing curve 4c of the load F decreases gently, and thus, the product F.multidot.v takes on an extremely high maximum value, as indicated by the second curve 6b.
A conventional gear device constructed as described above presents the following problems.
There is an increase in the product F.multidot.v of the load F acting on the teeth and the relative sliding velocity v at the area of contact of a pair of teeth, thereby increasing a frictional heat and sometimes resulting in scoring at the tooth surface.
Further, teeth which do not undergo a suitable tooth-profile correction are likely to be deflected by the intermeshing of the gears, which brings about a change in the rotation velocity of a driven gear, thereby inducing torsional vibration.
Calculation of thermal load capacity of cylindrical, bevel and hypoid gears
Part 1:
Evaluating the risk of scuffing Issued on Sep. 27, 1993 pp 1-54
(2) Mechanical Design Handbook Kyoritsu Shuppan Ltd.
Issued on Apr. 25, 1955 pp 10-1-10-56 Gear